Computing with Analyzed Shapes

Abstract

Shapes play an important role in many human activities, but are rarely seen in their natural form as raw and unanalyzed. Shapes are usually analyzed or structured in terms of their certain parts. Analyzed shapes or shape decompositions are central to this paper. Different shape decompositions are developed together with their algebras. The most interesting decompositions are the ones that could successfully be used as shape approximations. Two kinds of such decompositions: discrete and bounded are examined in greater detail.